Encyclopedia of Sparse Graph Codes

This is a database of sparse graph codes.
Properties recorded include the codes' parity check matrices,
their rates and minimum distances,
their empirical performance on the binary input Gaussian noise channel,
and histograms of decoding times.

These Codes and Related Data
are made freely available under the conditions that
(1) when they are used, the authors of the codes and the data
and this archive are acknowledged; (2) the authors of the
codes and data are not liable for any inaccuracies
in the materials presented here or any failure of
the codes to work as hoped.

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Note: there are more codes that I have simulated
that have not yet made it into this archive.
If you have any requests for additions, email me. With appropriate
incentives (eg financial support for my group), I can probably help.

Progressive Edge Growth construction attempts to maximize girth, and empirically gives very good codes. This is the best known regular Gallager code with these parameters (M,N,t) [Best in the sense of perfromance on AWGN, Wed 11/5/05]. The code is not quite regular in row-degree.

Progressive Edge Growth construction attempts to maximize girth, and empirically gives very good codes. This is the best known regular Gallager code with these parameters (M,N,t) [Best in the sense of perfromance on AWGN, Wed 11/5/05]. The code is not quite regular in row-degree.

Progressive Edge Growth construction attempts to maximize girth, and empirically gives very good codes. This is the best known code with these parameters (N,M). [Best in the sense of perfromance on AWGN, Wed 11/5/05]

Progressive Edge Growth construction attempts to maximize girth, and empirically gives very good codes. The best known code with these parameters (N,M). [Best in the sense of perfromance on AWGN, Wed 11/5/05]

This code was found by an intensive search using construction method 1A followed by manual pruning of two columns to remove the remaining overlaps greater than 1. It is the highest rate code I was able to make with column weight 4 and blocklength near 4376. It may be that this code is sailing too close to the wind, i.e., that its asymptotic performance for high snr is not as good as other Gallager codes. Nevertheless, in experiments so far this code competes well with RS and BCH codes.

This code is presented on page 221 of D J C MacKay (2003), and eq 13.41. I call it the pentagonful low-density parity-check code. The graph is called the Petersen graph, so maybe a good name for this code would be the (15,6) Petersen code. It has 12 words of weight 5.